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FLORHAM PARK, N.J. (AP) — There will be a moment during the NFL draft when Mike Tannenbaum gets antsy.

Whether it’s the first round or last, it happens every year with the New York Jets general manager.

Sensing a chance to improve his team, Tannenbaum will think about wheeling and dealing — and many times, he’ll act on the impulse. Just as he did to trade up for some of the team’s core players during the last few years, including Darrelle Revis, Mark Sanchez and Shonn Greene.

“I pride myself on being a good listener, and everyone in that room has a say in the process,” Tannenbaum said. “We look at trades as win-win. And hopefully the teams we’ve traded with feel the same.”

The Jets have 10 picks — including four compensatory picks for lost free agents — this year, starting with No. 16 overall in the first round Thursday night. And that’s a whole lot for Tannenbaum to deal with, especially considering that New York has had a total of 13 picks in the last three years.

“It has already been pointed out to me that it would be mathematically impossible to have less picks than we did in 2009, because with the four compensatories, I can’t trade them,” said a smiling Tannenbaum, referring to the three-player class the Jets had three years ago. “I really don’t know what we are going to do, but I do like the flexibility of the 10 picks even though we can’t trade four.”

New York certainly has plenty of holes on its roster after a relatively quiet run through free agency so far with safety LaRon Landry and wide receiver Chaz Schilens being their biggest signings. Oh, and there was also that headline-grabbing deal when they traded for quarterback Tim Tebow last month.

“We definitely have needs, but again I think some of the signings like LaRon take some pressure off at the safety position, for example,” Tannenbaum said. “And there’s some development from within. … Clearly when we modeled our team this year, we thought this draft was going to be important to add a couple of guys, and that hasn’t changed.”

The Jets have insisted Tebow will be the backup to Sanchez and be listed as a quarterback, although he will be used in a variety of roles on offense. That versatility, Tannenbaum said, could serve as a “subtle tiebreaker” when the Jets are trying to decide between players when they go on the clock.

But New York is likely to focus on defensive players early in the draft, just as they have in recent years. The Jets have gone with defense with their first-round pick in four of the last five drafts: Revis (2007), Vernon Gholston (2008), Kyle Wilson (2010) and Muhammad Wilkerson (2011). The only time they took an offensive player first in that span was when they traded way up and took Sanchez with the fifth overall selection.

Unless Alabama running back Trent Richardson or Notre Dame wide receiver Michael Floyd remain on the board when they pick, the Jets will be hoping Crimson Tide safety Mark Barron and linebacker Courtney Upshaw, defensive ends Melvin Ingram of South Carolina and Quinton Coples of North Carolina, or defensive tackle Dontari Poe of Memphis are available.

Barron would fill one of the Jets’ biggest needs as Landry and Eric Smith are the only safeties on the roster with significant NFL experience. The playmaking safety would likely see lots of playing time in Rex Ryan’s aggressive defense.

“He’s physical, he’s tough, he’s very bright, he’s a space player, he can make one-on-one tackles,” said Joey Clinkscales, the Jets’ vice president of college scouting. “He has a lot of the skillset that I think every team is looking for at the safety position. I’m not saying that he may or may not be the best fit for this team or any defense that’s running a true man-to-man system, but he has the skillset to really be effective in some of the things we do, and other teams as well.”

Despite finishing fifth in overall defense, Ryan’s group was hardly dominant — especially when it came to putting consistent pressure on opposing quarterbacks. New York’s 35 sacks ranked tied for 17th in the league, and Aaron Maybin led the team with just six. Bringing in Upshaw, Ingram or Coples would give the Jets a much-needed legitimate pass rusher.

“Coples is a phenomenal athlete,” Clinkscales said. “He probably played better as a junior than he did this season. Obviously, Ingram, this was his breakout year, he’s a one-year starter. And Courtney Upshaw, they won a national championship, he’s a physical, strong, aggressive player. They all have traits that you like.”

While Tannenbaum has had some major hits on draft day in his six years as GM, there have also been a few misses — most notably Gholston. The former Ohio State star zipped up teams’ charts with an incredible performance at the NFL combine and New York took him sixth overall in 2008, but he never panned out in three seasons with the Jets before being cut last offseason without having recorded a sack.

“Ultimately, that was my decision,” Tannenbaum said. “There were a lot of things we liked about Vernon: his measurables, production, and obviously it didn’t work out. Why it didn’t, we’ve looked at that quite a bit. … From where I stand in the world, it’s most important that we learn from it and do everything we can to make sure it doesn’t happen again.”

And that’s the responsibility Tannenbaum is charged with — anxious moments on draft day and all.

“This is the next step in our offseason,” he said. “Obviously it is an important step, but it certainly is not the last. We will never quit looking for players that can help this team win games.”

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